 Hello and welcome to the session. In this session we will discuss how to find equation of circle in coordinate plane. We can write equation of a circle in a coordinate plane if we know its radius and coordinates of its center. Suppose we have a circle with radius r and center with coordinates hk. Now let the ordered pair xy represents any point on the circle. We know that distance between any point on the circle to the center is radius of the circle. So, distance from the point with coordinates xy to the center with coordinates hk is equal to r. So, by distance formula we have square root of x minus h whole square plus y minus k whole square is equal to r. Now squaring both sides we get x minus h whole square plus y minus k whole square is equal to r square which is the standard equation of the circle with radius r and center with coordinates hk. Now if the center is at origin then the equation of the circle becomes x minus 0 whole square plus y minus 0 whole square is equal to r square which implies that x square plus y square is equal to r square. Let us discuss an example. Find the equation of the circle with center having coordinates 1 minus 5 and radius 2. Let us start its solution. We know that standard equation of the circle is given by x minus h whole square plus y minus k whole square is equal to r square where the ordered pair hk represents the center of the circle and r represents the radius of the circle. Now here we are given coordinates of center as 1 minus 5 and r as 2. So substituting r is equal to 2, h is equal to 1 and k is equal to minus 5 in this equation we get x minus 1 whole square plus y minus of minus 5 whole square is equal to 2 square. This implies that x minus 1 whole square plus y minus of minus 5 is y plus 5 whole square is equal to 4. So this is the required equation of the circle in standard form. Let us see another example where the circle with center o is given to us on the coordinate plane and we have to determine its equation. Here the center of the circle is at the origin that is point o with coordinates 00 and from this graph we can see that radius is equal to 2 units that is 2 square boxes and we know that equation of the circle with center at origin and radius r is given by x square plus y square is equal to r square. So we put r is equal to 2 in this equation and we get x square plus y square is equal to 2 square which implies that x square plus y square is equal to 4. This is the required equation of the given circle. Thus in this session we have learned how to find the equation of circle on the coordinate plane. This completes our session. Hope you enjoyed this session.